Short Distance Asymptotics for a Generalized Two-point Scaling Function in the Two-dimensional Ising Model
In the 1977 paper of McCoy et al. (J. Math. Phys. 18, 1058–1092, 1977) it was shown that the limiting two-point correlation function in the two-dimensional Ising model is related to a second order nonlinear Painlevé function. This result identified the scaling function as a tau-function and the corresponding connection problem was solved by Tracy (Commun. Math. Phys. 142, 297–311, 1991), see also the works by Tracy and Widom (Commun. Math. Phys. 190, 697–721, 1998). Here we present the solution to a certain generalized version of the above connection problem which is obtained through a refinement of the techniques chosen in Bothner (J. Stat. Phys. 170, 672–683, 2018).
KeywordsIsing model Generalized 2-point function Short distance expansion
Mathematics Subject Classification (2010)Primary 82B20 Secondary 70S05 34M55
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